More classes of permutation hexanomials and pentanomials over finite fields with even characteristic

In this paper, we further push the studies on permutation polynomials over the finite fields Fq2 with q=2m. We find the coefficients of f(x)=x+a1xs1(q−1)+1+a2xs2(q−1)+1+a3xs3(q−1)+1+a4xs4(q−1)+1+a5xs5(q−1)+1 over Fq2 that lead f(x) to be a permutation for (s1,s2,s3,s4)=(14,12,1,34) in case of a5=0,...

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Bibliographic Details
Published in:Finite fields and their applications 2023-10, Vol.91, p.102250, Article 102250
Main Authors: Zhang, Tongliang, Zheng, Lijing, Hao, Xinghui
Format: Article
Language:English
Subjects:
Finite field
Permutation hexanomial and pentanomial
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Summary:In this paper, we further push the studies on permutation polynomials over the finite fields Fq2 with q=2m. We find the coefficients of f(x)=x+a1xs1(q−1)+1+a2xs2(q−1)+1+a3xs3(q−1)+1+a4xs4(q−1)+1+a5xs5(q−1)+1 over Fq2 that lead f(x) to be a permutation for (s1,s2,s3,s4)=(14,12,1,34) in case of a5=0, and find more new (si) such that f(x) is a permutation hexanomial of Fq2 with coefficients in F4. Some well-known results are covered by our results. The numerical results suggest that the sufficient conditions we find in the first class of permutation pentanomials are also necessary.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2023.102250